The number of bacteria in a certain culture doubles every hour.

Question:

The number of bacteria in a certain culture doubles every hour. If there were 30 bacteria present in the culture originally, how many bacteria will be present at the end of $2^{\text {nd }}$ hour, $4^{\text {th }}$ hour and $n^{\text {th }}$ hour?

Solution:

It is given that the number of bacteria doubles every hour. Therefore, the number of bacteria after every hour will form a G.P.

Here, $a=30$ and $r=2$

$\therefore a_{3}=a r^{2}=(30)(2)^{2}=120$

Therefore, the number of bacteria at the end of $2^{\text {nd }}$ hour will be 120 .

$a_{5}=a r^{4}=(30)(2)^{4}=480$

The number of bacteria at the end of $4^{\text {th }}$ hour will be 480 .

$a_{n+1}=a r^{n}=(30) 2^{n}$

Thus, number of bacteria at the end of $n^{\text {th }}$ hour will be $30(2)^{n}$.

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